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Unformatted text preview: Confidence Intervals A confidence interval provides a simple summary of how precisely a parameter, denoted , is estimated. In many situations, a (1 - )100% confidence interval is of the form ^ ( - s t/2 , ^ where ^ is an estimate of s is its standard error ^ t/2 is the upper /2th quantile from a distribution like the normal or t ^ + s t/2 ) ^ s is usually inversely proportional to the square ^ root of the sample size, so the interval is narrower for larger samples t/2 is larger for smaller or larger confidence level, so a 99% confidence interval is wider than a 95% confidence interval the interval is constructed so that in advance there is probability 1 - that it includes the true value of the parameter once we get the data and evaluate the interval endpoints we don't know whether or not the interval contains the true parameter but we are confident that it does the figure below shows 95% confidence intervals for the mean constructed using 25 different random samples 25 Confidence intervals from normal samples of size 20 u most of these intervals do contain the true mean but two do not ...
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This note was uploaded on 03/27/2012 for the course ECON 2280 taught by Professor Daniel during the Spring '12 term at Dalhousie.
- Spring '12